Jess owns a firm that uses labour (L) and capital (C) to sell widgets (X), according to the following production function: X = F(L,C) = ln(L) + ln(C) Jesse buys her factors and sells her output in perfectly competitive markets. The market prices for L, C and W are a, r and p, respectively.  What is the firm’s profit function.  What is the  firm's marginal product of labour , marginal product of capital  and marginal rate of technical substitution  Does the firm exhibit a diminishing marginal product of capital?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Jess owns a firm that uses labour (L) and capital (C) to sell widgets (X), according to the following production function:

X = F(L,C) = ln(L) + ln(C)

Jesse buys her factors and sells her output in perfectly competitive markets. The market prices for L, C and W are a, r and p, respectively. 

  1. What is the firm’s profit function. 
  2. What is the  firm's marginal product of labour , marginal product of capital  and marginal rate of technical substitution 
  3. Does the firm exhibit a diminishing marginal product of capital?
  4. What is the firms demand functions for labour and capital. 
  5. Say the central bank decides to increase interest rates, causing ? to go up. What effect will this have on the firm’s use of L and C? What effect will it have on output (X) and profits?
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